Probability Question

Question

A thermostat is set on 70 degrees. A room temperature is distributed normally with the standard deviation of .1. What is the probability that the room temperature will be higher than 70.2 degrees?

Answer 1

Mean = 70

Standard Deviation = .1

Value = 70.2

Hopefully that helps clarify things a bit. Anyway, we now want to know how many standard deviations away from the mean our value is (z-score). The formula is:

(Value - Mean)/Standard Deviation

(70.2 - 70) / .1 = 2

The value is 2 standard deviations away. That means 97.5% of values lie below it. So, only 2.5% of values lie above.

Therefore, our answer is 2.5%.